Dividing decimals
Scale both quantities to make a divisor whole, then check by multiplication.
Before you begin
- Long division
- Multiplying by powers of ten
Preserve the quotient by scaling both numbers
Dividing asks how many groups of one size fit into another quantity. Multiplying both the dividend and divisor by the same nonzero number leaves that number of groups unchanged. For 4.2 ÷ 0.6, convert both amounts into tenths to get 42 ÷ 6. Moving the decimal point in only one number would change the question.
Continue through decimal places
Once the divisor is whole, use division place by place and carry the decimal point into the quotient. Append zeros to the dividend if needed. Check the answer by multiplying it by the original divisor, not only the scaled one. A divisor smaller than one can give a quotient larger than the dividend because many small groups fit into a quantity.
Worked example
Calculate 7.56 ÷ 0.18.
Show the worked solution
- Multiply both numbers by 100: 756 ÷ 18.
- 18 × 40 = 720, leaving 36; 18 × 2 = 36, so the quotient is 42.
- Check using the original values: 42 × 0.18 = 7.56.
42.
Try it yourself
What is 3.6 ÷ 0.4?
Common mistakes
- Scale the dividend and divisor together.
- Estimate whether the quotient should be larger or smaller than the dividend.
What can you explain now?
How many metres of ribbon can you buy for $9.45 if it costs $1.5 per metre?
Compare with the explanation
6.3 m.
9.45 ÷ 1.5 = 94.5 ÷ 15 = 6.3. Multiplying 6.3 m by $1.5 per metre gives $9.45.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗